Download Prentice Hall Algebra 2 Common Core Edition

A Correlation of
Prentice Hall
Algebra 2
Common Core Edition
to the
Alabama Course of Study
Mathematics
Algebra 2 with Trigonometry
Prentice Hall Algebra 2, Common Core Edition
Correlated to the Alabama Course of Study Mathematics - Algebra 2 with Trigonometry
NUMBER AND QUANTITY
THE COMPLEX NUMBER SYSTEM
Perform arithmetic operations with complex numbers.
Prentice Hall Algebra 2
Common Core Edition
(Chapter-Lesson)
Alabama Course of Study: Mathematics
Algebra 2 with Trigonometry
1. Know there is a complex number i such that i2 = −1, and
every complex number has the form a + bi with a and b
real. [N.CN.1]
4-8
2. Use the relation i2 = –1 and the commutative,
associative, and distributive properties to add, subtract,
and multiply complex numbers. [N.CN.2]
4-8
Use complex numbers in polynomial identities and equations. (Polynomials with real
coefficients.)
3. Solve quadratic equations with real coefficients that have
complex solutions. [N.CN.7]
4-8, 5-5, 5-6
4. (+) Extend polynomial identities to the complex
numbers. [N.CN.8]
4-8, 5-5, 5-6
5. (+) Know the Fundamental Theorem of Algebra; show
that it is true for quadratic polynomials. [N.CN.9]
5-6
ALGEBRA
SEEING STRUCTURE IN EXPRESSIONS
Interpret the structure of expressions. (Polynomial and rational.)
6. Interpret expressions that represent a quantity in terms
of its context.* [A.SSE.1]
5-2, 8-4
a. Interpret parts of an expression, such as terms, factors,
and coefficients. [A.SSE.1.a]
4-5, 5-1, 5-2, 8-4
b. Interpret complicated expressions by viewing one or
more of their parts as a single entity. [A.SSE.1.b]
1-6, 7-1, 7-2, 7-3, 8-4
7. Use the structure of an expression to identify ways to
rewrite it. [A.SSE.2]
4-4, 5-3, 6-1, 6-2, 6-3, 8-4
Write expressions in equivalent forms to solve problems.
8. Derive the formula for the sum of a finite geometric
series (when the common ratio is not 1), and use the
formula to solve problems.* [A.SSE.4]
2
CB = Concept Byte
* Indicates a standard that relates to modeling.
9-5, CB 9-5
Prentice Hall Algebra 2, Common Core Edition
Correlated to the Alabama Course of Study Mathematics - Algebra 2 with Trigonometry
ARITHMETIC WITH POLYNOMIALS AND RATIONAL EXPRESSIONS
Perform arithmetic operations on polynomials. (Beyond quadratic.)
Prentice Hall Algebra 2
Common Core Edition
(Chapter-Lesson)
Alabama Course of Study: Mathematics
Algebra 2 with Trigonometry
9. Understand that polynomials form a system analogous to
the integers, namely, they are closed under the operations
of addition, subtraction, and multiplication; add, subtract,
and multiply polynomials. [A.APR.1]
5-4
Understand the relationship between zeros and factors of polynomials.
10. Know and apply the Remainder Theorem: For a
polynomial p(x) and a number a, the remainder on division
by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor
of p(x). [A.APR.2]
5-4
11. Identify zeros of polynomials when suitable
factorizations are available, and use the zeros to construct
a rough graph of the function defined by the polynomial.
[A.APR.3]
4-5, 5-2, 5-6, CB 5-7
Use polynomial identities to solve problems.
12. Prove polynomial identities and use them to describe
numerical relationships. [A.APR.4]
CB 5-5
13. (+) Know and apply the Binomial Theorem for the
expansion of (x + y)n in powers of x and y for a positive
integer n, where x and y are any numbers, with coefficients
determined for example by Pascal’s Triangle. [A.APR.5]
5-7
Rewrite rational expressions. (Linear and quadratic denominators.)
14. Rewrite simple rational expressions in different forms;
write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x),
b(x), q(x), and r(x) are polynomials with the degree of r(x)
less than the degree of b(x), using inspection, long division,
or, for the more complicated examples, a computer algebra
system. [A.APR.6]
5-4, 8-6
15. (+) Understand that rational expressions form a system
analogous to the rational numbers, closed under addition,
subtraction, multiplication, and division by a nonzero
rational expression; add, subtract, multiply, and divide
rational expressions. [A.APR.7]
8-5, 8-6
3
CB = Concept Byte
* Indicates a standard that relates to modeling.
Prentice Hall Algebra 2, Common Core Edition
Correlated to the Alabama Course of Study Mathematics - Algebra 2 with Trigonometry
CREATING EQUATIONS
Create equations that describe numbers or relationships. (Equations using all available
types of expressions, including simple root functions.)
Prentice Hall Algebra 2
Common Core Edition
(Chapter-Lesson)
Alabama Course of Study: Mathematics
Algebra 2 with Trigonometry
16. Create equations and inequalities in one variable and
use them to solve problems. Include equations arising from
linear and quadratic functions, and simple rational and
exponential functions. [A.CED.1]
1-4, 1-5, 1-6, 4-1, 4-5, 8-6, CB 8-1
17. Create equations in two or more variables to represent
relationships between quantities; graph equations on
coordinate axes with labels and scales. [A.CED.2]
2-2, 2-3, 2-4, 2-5, 2-8, 3-1, 3-2, 4-2,
CB 4-5, 7-1, 7-2, 8-1, 8-2, 8-3
18. Represent constraints by equations or inequalities, and
by systems of equations and/or inequalities, and interpret
solutions as viable or non-viable options in a modeling
context. [A.CED.3]
3-1, 3-2, 3-3, 3-4, CB 3-4, 4-9, CB 7-6
19. Rearrange formulas to highlight a quantity of interest,
using the same reasoning as in solving equations.
[A.CED.4]
1-4, 6-5, 8-1
REASONING WITH EQUATIONS AND INEQUALITIES
Understand solving equations as a process of reasoning and explain the reasoning. (Simple
rational and radical.)
20. Solve simple rational and radical equations in one
variable, and give examples showing how extraneous
solutions may arise. [A.REI.2]
6-5, 8-6
Represent and solve equations and inequalities graphically. (Combine polynomial, rational,
radical, absolute value, and exponential functions.)
21. Explain why the x-coordinates of the points where the
graphs of the equations y = f(x) and y = g(x) intersect are
the solutions of the equation f(x) = g(x); find the solutions
approximately, e.g., using technology to graph the
functions, make tables of values, or find successive
approximations. Include cases where f(x) and/or g(x) are
linear, polynomial, rational, absolute value, exponential,
and logarithmic functions.* [A.REI.11]
4
CB = Concept Byte
* Indicates a standard that relates to modeling.
3-1, 5-3, 7-5, CB 7-6, 8-6
Prentice Hall Algebra 2, Common Core Edition
Correlated to the Alabama Course of Study Mathematics - Algebra 2 with Trigonometry
FUNCTIONS
INTERPRETING FUNCTIONS
Interpret functions that arise in applications in terms of the context. (Emphasize selection of
appropriate models.)
22. For a function that models a relationship between two
quantities, interpret key features of graphs and tables in
terms of the quantities, and sketch graphs showing key
features given a verbal description of the relationship. Key
features include: intercepts; intervals where the function is
increasing, decreasing, positive, or negative; relative
maximums and minimums; symmetries; end behavior;
and periodicity.* [F.IF.4]
2-3, 2-5, 4-1, 4-2, 4-3, 5-1, 5-8,
CB 7-3, 13-1, 13-4, 13-5
23. Relate the domain of a function to its graph and, where
applicable, to the quantitative relationship it describes.
*[F.IF.5]
4-3, 5-8
24. Calculate and interpret the average rate of change of a
function (presented symbolically or as a table) over a
specified interval. Estimate the rate of change from a
graph.* [F.IF.6]
2-5, 4-1, 4-2, CB 4-3, 5-8
Analyze functions using different representations, (Focus on using key features to guide
selection of appropriate type of model function.)
25. Graph functions expressed symbolically, and show key
features of the graph, by hand in simple cases and using
technology for more complicated cases.* [F-IF7]
2-3, 2-4, 2-7, 2-6, 4-1, 4-2, 5-1, 5-2, 58, 6-8, 7-2, 8-3, CB 2-4, CB 8-2
a. Graph square root, cube root, and piecewise-defined
functions, including step functions and absolute value
functions. [F.IF.7.b]
2-7, 2-8, 6-8, CB 2-4
b. Graph polynomial functions, identifying zeros when
suitable factorizations are available, and showing end
behavior. [F.IF.7.c]
5-1, 5-2, 5-9
c. Graph exponential and logarithmic functions, showing
intercepts and end behavior, and trigonometric functions,
showing period, midline, and amplitude. [F.IF.7.e]
7-1, 7-2, 7-3, 13-4, 13-5, 13-6, 13-7,
13-8, CB 7-5
5
CB = Concept Byte
* Indicates a standard that relates to modeling.
Prentice Hall Algebra 2, Common Core Edition
Correlated to the Alabama Course of Study Mathematics - Algebra 2 with Trigonometry
Prentice Hall Algebra 2
Common Core Edition
(Chapter-Lesson)
Alabama Course of Study: Mathematics
Algebra 2 with Trigonometry
26. Write a function defined by an expression in different
but equivalent forms to reveal and explain different
properties of the function. [F.IF.8]
2-4, 4-2, 5-9, 6-8, 7-2, 7-3, CB 7-5
27. Compare properties of two functions each represented
in a different way (algebraically, graphically, numerically in
tables, or by verbal descriptions). [F.IF.9]
2-4, 4-2, 5-9, 7-3
BUILDING FUNCTIONS
Build a function that models a relationship between two quantities. (Include all types of
functions studied.)
28. Write a function that describes a relationship between
two quantities.* [F.BF.1]
2-2, 2-5, 4-2, 5-2, 6-6, 7-2, 8-2, 8-3
a. Combine standard function types using arithmetic
operations. [F.BF.1.b]
6-6, 7-2, 8-3
Build new functions from existing functions. (Include simple radical, rational, and
exponential functions; emphasize common effect of each transformation across function
types.)
29. Identify the effect on the graph of replacing f(x) by f(x)
+ k, k f(x), f(kx), and f(x + k) for specific values of k (both
positive and negative); find the value of k given the graphs.
Experiment with cases and illustrate an explanation of the
effects on the graph using technology. Include recognizing
even and odd functions from their graphs and algebraic
expressions for them. [F.BF.3]
2-6, 2-7, 4-1, 5-9, 8-2
30. Solve an equation of the form f(x) = c for a simple
function f that has an inverse and write an expression for
the inverse. [F.BF.4.a]
6-7, 7-3
6
CB = Concept Byte
* Indicates a standard that relates to modeling.
Prentice Hall Algebra 2, Common Core Edition
Correlated to the Alabama Course of Study Mathematics - Algebra 2 with Trigonometry
LINEAR AND EXPONENTIAL MODELS
Construct and compare linear and exponential models and solve problems. (Logarithms as
solutions for exponentials.)
Prentice Hall Algebra 2
Common Core Edition
(Chapter-Lesson)
Alabama Course of Study: Mathematics
Algebra 2 with Trigonometry
31. For exponential models, express as a logarithm the
solution to abct = d where a, c, and d are numbers and the
base b is 2, 10, or e; evaluate the logarithm using
technology. [F.LE.4]
7-5, 7-6
TRIGONOMETRIC FUNCTIONS
Extend the domain of trigonometric functions using the unit circle.
32. Understand radian measure of an angle as the length of
the arc on the unit circle subtended by the angle. [F.TF.1]
13-3
33. Explain how the unit circle in the coordinate plane
enables the extension of trigonometric functions to all real
numbers, interpreted as radian measures of angles
traversed counterclockwise around the unit circle. [F.TF.2]
13-4, 13-5, 13-6
34. Define the six trigonometric functions using ratios of
the sides of a right triangle, coordinates on the unit circle,
and the reciprocal of other functions.
14-3
Model periodic phenomena with trigonometric functions.
35. Choose trigonometric functions to model periodic
phenomena with specified amplitude, frequency, and
midline. [F.TF.5]
13-4, 13-5, 13-6, 13-7
Prove and apply trigonometric identities.
36. Prove the Pythagorean identity sin2 (θ) + cos2 (θ) = 1
and use it to calculate trigonometric ratios. [F.TF.8]
7
CB = Concept Byte
* Indicates a standard that relates to modeling.
14-1
Prentice Hall Algebra 2, Common Core Edition
Correlated to the Alabama Course of Study Mathematics - Algebra 2 with Trigonometry
STATISTICS AND PROBABILITY
INTERPRETING CATEGORICAL AND QUANTITATIVE DATA
Summarize, represent, and interpret data on two categorical and quantitative variables.
Prentice Hall Algebra 2
Common Core Edition
(Chapter-Lesson)
Alabama Course of Study: Mathematics
Algebra 2 with Trigonometry
37. Use the mean and standard deviation of a data set to fit
it to a normal distribution and to estimate population
percentages. Recognize that there are data sets for which
such a procedure is not appropriate. Use calculators,
spreadsheets, and tables to estimate areas under the
normal curve. [S.ID.4]
11-7, 11-10
MAKING INFERENCES AND JUSTIFYING CONCLUSIONS
Understand and evaluate random processes underlying statistical experiments.
38. Understand statistics as a process for making
inferences to be made about population parameters based
on a random sample from that population. [S.IC.1]
11-8
39. Decide if a specified model is consistent with results
from a given data-generating process, e.g., using
simulation. [S.IC.2]
CB 11-3
Make inferences and justify conclusions from sample surveys, experiments, and
observational studies.
40. Recognize the purposes of and differences among
sample surveys, experiments, and observational studies;
explain how randomization relates to each. [S.IC.3]
11-8
41. Use data from a sample survey to estimate a population
mean or proportion; develop a margin of error through the
use of simulation models for random sampling. [S.IC.4]
11-8, CB 11-10a
42. Use data from a randomized experiment to compare
two treatments; use simulations to decide if differences
between parameters are significant. [S.IC.5]
CB 11-10b
43. Evaluate reports based on data. [S.IC.6]
11-6, 11-7, 11-8
USING PROBABILITY TO MAKE DECISIONS
Use probability to evaluate outcomes of decisions. (Include more complex situations.)
44. (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [S.MD.6]
11-5
45. (+) Analyze decisions and strategies using probability
concepts (e.g., product testing, medical testing, pulling a
hockey goalie at the end of a game). [S.MD.7]
11-5
8
CB = Concept Byte
* Indicates a standard that relates to modeling.